LMFDB - Space of modular forms of level 5445, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 5445 = 3^{2} \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5445.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 56 $
Sturm bound:			$1584$
Trace bound:			$14$
Distinguishing $T_p$:			$2$, $7$, $23$, $53$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(5445))$.

	Total	New	Old
Modular forms	840	181	659
Cusp forms	745	181	564
Eisenstein series	95	0	95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$3$	$5$	$11$	Fricke	Dim.
$+$	$+$	$+$	$+$	$18$
$+$	$+$	$-$	$-$	$18$
$+$	$-$	$+$	$-$	$18$
$+$	$-$	$-$	$+$	$18$
$-$	$+$	$+$	$-$	$30$
$-$	$+$	$-$	$+$	$25$
$-$	$-$	$+$	$+$	$24$
$-$	$-$	$-$	$-$	$30$
Plus space			$+$	$85$
Minus space			$-$	$96$

Trace form

$ 181q - q^{2} + 175q^{4} - q^{5} - 4q^{7} - 9q^{8} + O(q^{10}) $

$ 181q - q^{2} + 175q^{4} - q^{5} - 4q^{7} - 9q^{8} - 3q^{10} - 10q^{13} - 24q^{14} + 159q^{16} + 6q^{17} - 12q^{19} - 7q^{20} - 8q^{23} + 181q^{25} + 10q^{26} + 12q^{28} - 6q^{29} + 4q^{31} - 29q^{32} + 6q^{34} + 4q^{35} - 2q^{37} + 12q^{38} - 3q^{40} + 14q^{41} - 16q^{43} + 28q^{46} - 28q^{47} + 169q^{49} - q^{50} + 10q^{52} - 26q^{53} - 4q^{56} + 50q^{58} - 16q^{59} + 6q^{61} + 32q^{62} + 191q^{64} + 2q^{65} - 20q^{67} + 66q^{68} + 16q^{70} + 12q^{71} - 22q^{73} - 14q^{74} + 44q^{76} - 32q^{79} + q^{80} + 82q^{82} - 14q^{85} + 32q^{86} - 42q^{89} - 48q^{91} - 4q^{92} + 76q^{94} + 12q^{95} - 114q^{97} + 55q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(5445))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	5	11	$q$-expansion
5445.2.a.a	$1$	$43.479$	$\Q$	None	$-2$	$0$	$-1$	$-3$	$+$	$+$	$-$	$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$
5445.2.a.b	$1$	$43.479$	$\Q$	None	$-2$	$0$	$1$	$3$	$+$	$-$	$-$	$q-2q^{2}+2q^{4}+q^{5}+3q^{7}-2q^{10}+\cdots$
5445.2.a.c	$1$	$43.479$	$\Q$	None	$-1$	$0$	$-1$	$0$	$-$	$+$	$-$	$q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{13}+\cdots$
5445.2.a.d	$1$	$43.479$	$\Q$	None	$-1$	$0$	$-1$	$3$	$-$	$+$	$-$	$q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots$
5445.2.a.e	$1$	$43.479$	$\Q$	None	$-1$	$0$	$1$	$2$	$-$	$-$	$+$	$q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots$
5445.2.a.f	$1$	$43.479$	$\Q$	None	$0$	$0$	$1$	$-1$	$-$	$-$	$-$	$q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots$
5445.2.a.g	$1$	$43.479$	$\Q$	None	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots$
5445.2.a.h	$1$	$43.479$	$\Q$	None	$1$	$0$	$-1$	$-3$	$-$	$+$	$-$	$q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots$
5445.2.a.i	$1$	$43.479$	$\Q$	None	$1$	$0$	$-1$	$0$	$-$	$+$	$-$	$q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{13}+\cdots$
5445.2.a.j	$1$	$43.479$	$\Q$	None	$1$	$0$	$1$	$-2$	$-$	$-$	$+$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
5445.2.a.k	$1$	$43.479$	$\Q$	None	$2$	$0$	$-1$	$3$	$+$	$+$	$-$	$q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots$
5445.2.a.l	$1$	$43.479$	$\Q$	None	$2$	$0$	$1$	$-3$	$+$	$-$	$-$	$q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots$
5445.2.a.m	$2$	$43.479$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$2$	$4$	$-$	$-$	$-$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots$
5445.2.a.n	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$-2$	$-4$	$+$	$+$	$-$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots$
5445.2.a.o	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$2$	$2$	$-$	$-$	$-$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots$
5445.2.a.p	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$2$	$4$	$+$	$-$	$-$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+2q^{7}+\cdots$
5445.2.a.q	$2$	$43.479$	$\Q(\sqrt{3}) $	None	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$q-2q^{4}+q^{5}-\beta q^{7}+4q^{16}-2\beta q^{17}+\cdots$
5445.2.a.r	$2$	$43.479$	$\Q(\sqrt{3}) $	None	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots$
5445.2.a.s	$2$	$43.479$	$\Q(\sqrt{3}) $	None	$0$	$0$	$2$	$-4$	$-$	$-$	$-$	$q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
5445.2.a.t	$2$	$43.479$	$\Q(\sqrt{3}) $	None	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}+\beta q^{10}+\cdots$
5445.2.a.u	$2$	$43.479$	$\Q(\sqrt{3}) $	None	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$q+\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
5445.2.a.v	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$1$	$0$	$-2$	$4$	$+$	$+$	$-$	$q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots$
5445.2.a.w	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$1$	$0$	$2$	$-4$	$+$	$-$	$-$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2q^{7}+\cdots$
5445.2.a.x	$2$	$43.479$	$\Q(\sqrt{5}) $	None	$1$	$0$	$2$	$-2$	$-$	$-$	$-$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots$
5445.2.a.y	$2$	$43.479$	$\Q(\sqrt{2}) $	None	$2$	$0$	$2$	$4$	$-$	$-$	$-$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots$
5445.2.a.z	$3$	$43.479$	3.3.148.1	None	$-1$	$0$	$-3$	$0$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.ba	$3$	$43.479$	3.3.469.1	None	$-1$	$0$	$-3$	$3$	$-$	$+$	$-$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.bb	$3$	$43.479$	3.3.404.1	None	$-1$	$0$	$3$	$-1$	$-$	$-$	$-$	$q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.bc	$3$	$43.479$	3.3.469.1	None	$1$	$0$	$-3$	$-3$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.bd	$3$	$43.479$	3.3.404.1	None	$1$	$0$	$3$	$1$	$-$	$-$	$-$	$q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.be	$4$	$43.479$	4.4.725.1	None	$-5$	$0$	$4$	$-2$	$-$	$-$	$+$	$q+(-2+\beta _{1}+\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
5445.2.a.bf	$4$	$43.479$	4.4.725.1	None	$-3$	$0$	$-4$	$6$	$-$	$+$	$-$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
5445.2.a.bg	$4$	$43.479$	4.4.2525.1	None	$-3$	$0$	$-4$	$11$	$-$	$+$	$+$	$q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots$
5445.2.a.bh	$4$	$43.479$	4.4.48704.2	None	$-2$	$0$	$4$	$-4$	$+$	$-$	$-$	$q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots$
5445.2.a.bi	$4$	$43.479$	4.4.725.1	None	$-1$	$0$	$4$	$3$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5445.2.a.bj	$4$	$43.479$	$\Q(\zeta_{15})^+$	None	$-1$	$0$	$-4$	$0$	$-$	$+$	$+$	$q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
5445.2.a.bk	$4$	$43.479$	4.4.5725.1	None	$-1$	$0$	$4$	$-8$	$-$	$-$	$+$	$q+(\beta _{1}-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots$
5445.2.a.bl	$4$	$43.479$	$\Q(\sqrt{3}, \sqrt{7})$	None	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{5}+2\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots$
5445.2.a.bm	$4$	$43.479$	4.4.27648.1	None	$0$	$0$	$-4$	$0$	$+$	$+$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots$
5445.2.a.bn	$4$	$43.479$	4.4.27648.1	None	$0$	$0$	$4$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots$
5445.2.a.bo	$4$	$43.479$	4.4.8112.1	None	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots$
5445.2.a.bp	$4$	$43.479$	4.4.725.1	None	$1$	$0$	$4$	$-3$	$-$	$-$	$+$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5445.2.a.bq	$4$	$43.479$	$\Q(\zeta_{15})^+$	None	$1$	$0$	$-4$	$0$	$-$	$+$	$-$	$q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$
5445.2.a.br	$4$	$43.479$	4.4.5725.1	None	$1$	$0$	$4$	$8$	$-$	$-$	$-$	$q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
5445.2.a.bs	$4$	$43.479$	4.4.48704.2	None	$2$	$0$	$-4$	$-4$	$+$	$+$	$-$	$q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
5445.2.a.bt	$4$	$43.479$	4.4.725.1	None	$3$	$0$	$-4$	$-6$	$-$	$+$	$+$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
5445.2.a.bu	$4$	$43.479$	4.4.2525.1	None	$3$	$0$	$-4$	$-11$	$-$	$+$	$-$	$q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots$
5445.2.a.bv	$4$	$43.479$	4.4.725.1	None	$5$	$0$	$4$	$2$	$-$	$-$	$-$	$q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
5445.2.a.bw	$6$	$43.479$	6.6.74043072.1	None	$0$	$0$	$-6$	$0$	$+$	$+$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots$
5445.2.a.bx	$6$	$43.479$	6.6.27433728.1	None	$0$	$0$	$-6$	$0$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots$
5445.2.a.by	$6$	$43.479$	6.6.74043072.1	None	$0$	$0$	$6$	$0$	$+$	$-$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots$
5445.2.a.bz	$6$	$43.479$	6.6.437199552.1	None	$0$	$0$	$-6$	$0$	$-$	$+$	$+$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.ca	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-4$	$0$	$-8$	$8$	$+$	$+$	$+$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
5445.2.a.cb	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-4$	$0$	$8$	$-8$	$+$	$-$	$-$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
5445.2.a.cc	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$4$	$0$	$-8$	$-8$	$+$	$+$	$-$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots$
5445.2.a.cd	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$4$	$0$	$8$	$8$	$+$	$-$	$+$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(5445))$ into lower level spaces

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Elliptic curves over $\Q$
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Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5445.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(1584\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(23\), \(53\)

\(3\)	\(5\)	\(11\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(18\)
\(+\)	\(+\)	\(-\)	\(-\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(30\)
\(-\)	\(+\)	\(-\)	\(+\)	\(25\)
\(-\)	\(-\)	\(+\)	\(+\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)	\(30\)
Plus space			\(+\)	\(85\)
Minus space			\(-\)	\(96\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5445))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5445))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	5445.2.a

Level	$5445$
Weight	$2$
Character orbit	5445.a
Rep. character	$\chi_{5445}(1,\cdot)$
Character field	$\Q$
Dimension	$181$
Newform subspaces	$56$
Sturm bound	$1584$
Trace bound	$14$

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	5	11	$q$-expansion
5445.2.a.a	\(1\)	\(43.479\)	\(\Q\)	None	\(-2\)	\(0\)	\(-1\)	\(-3\)	\(+\)	\(+\)	\(-\)	\(q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.b	\(1\)	\(43.479\)	\(\Q\)	None	\(-2\)	\(0\)	\(1\)	\(3\)	\(+\)	\(-\)	\(-\)	\(q-2q^{2}+2q^{4}+q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.c	\(1\)	\(43.479\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{13}+\cdots\)
5445.2.a.d	\(1\)	\(43.479\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(3\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}+3q^{7}+3q^{8}+q^{10}+\cdots\)
5445.2.a.e	\(1\)	\(43.479\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(2\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots\)
5445.2.a.f	\(1\)	\(43.479\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
5445.2.a.g	\(1\)	\(43.479\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
5445.2.a.h	\(1\)	\(43.479\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
5445.2.a.i	\(1\)	\(43.479\)	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{13}+\cdots\)
5445.2.a.j	\(1\)	\(43.479\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
5445.2.a.k	\(1\)	\(43.479\)	\(\Q\)	None	\(2\)	\(0\)	\(-1\)	\(3\)	\(+\)	\(+\)	\(-\)	\(q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots\)
5445.2.a.l	\(1\)	\(43.479\)	\(\Q\)	None	\(2\)	\(0\)	\(1\)	\(-3\)	\(+\)	\(-\)	\(-\)	\(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
5445.2.a.m	\(2\)	\(43.479\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(2\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots\)
5445.2.a.n	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(-2\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots\)
5445.2.a.o	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(2\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots\)
5445.2.a.p	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(2\)	\(4\)	\(+\)	\(-\)	\(-\)	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.q	\(2\)	\(43.479\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-2q^{4}+q^{5}-\beta q^{7}+4q^{16}-2\beta q^{17}+\cdots\)
5445.2.a.r	\(2\)	\(43.479\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
5445.2.a.s	\(2\)	\(43.479\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(-\)	\(-\)	\(q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.t	\(2\)	\(43.479\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.u	\(2\)	\(43.479\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
5445.2.a.v	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(0\)	\(-2\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots\)
5445.2.a.w	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(0\)	\(2\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
5445.2.a.x	\(2\)	\(43.479\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(0\)	\(2\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots\)
5445.2.a.y	\(2\)	\(43.479\)	\(\Q(\sqrt{2}) \)	None	\(2\)	\(0\)	\(2\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots\)
5445.2.a.z	\(3\)	\(43.479\)	3.3.148.1	None	\(-1\)	\(0\)	\(-3\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ba	\(3\)	\(43.479\)	3.3.469.1	None	\(-1\)	\(0\)	\(-3\)	\(3\)	\(-\)	\(+\)	\(-\)	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bb	\(3\)	\(43.479\)	3.3.404.1	None	\(-1\)	\(0\)	\(3\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bc	\(3\)	\(43.479\)	3.3.469.1	None	\(1\)	\(0\)	\(-3\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.bd	\(3\)	\(43.479\)	3.3.404.1	None	\(1\)	\(0\)	\(3\)	\(1\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.be	\(4\)	\(43.479\)	4.4.725.1	None	\(-5\)	\(0\)	\(4\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+(-2+\beta _{1}+\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bf	\(4\)	\(43.479\)	4.4.725.1	None	\(-3\)	\(0\)	\(-4\)	\(6\)	\(-\)	\(+\)	\(-\)	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bg	\(4\)	\(43.479\)	4.4.2525.1	None	\(-3\)	\(0\)	\(-4\)	\(11\)	\(-\)	\(+\)	\(+\)	\(q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots\)
5445.2.a.bh	\(4\)	\(43.479\)	4.4.48704.2	None	\(-2\)	\(0\)	\(4\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bi	\(4\)	\(43.479\)	4.4.725.1	None	\(-1\)	\(0\)	\(4\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bj	\(4\)	\(43.479\)	\(\Q(\zeta_{15})^+\)	None	\(-1\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bk	\(4\)	\(43.479\)	4.4.5725.1	None	\(-1\)	\(0\)	\(4\)	\(-8\)	\(-\)	\(-\)	\(+\)	\(q+(\beta _{1}-\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5445.2.a.bl	\(4\)	\(43.479\)	\(\Q(\sqrt{3}, \sqrt{7})\)	None	\(0\)	\(0\)	\(4\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{3}q^{2}-\beta _{2}q^{4}+q^{5}+2\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
5445.2.a.bm	\(4\)	\(43.479\)	4.4.27648.1	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots\)
5445.2.a.bn	\(4\)	\(43.479\)	4.4.27648.1	None	\(0\)	\(0\)	\(4\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots\)
5445.2.a.bo	\(4\)	\(43.479\)	4.4.8112.1	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots\)
5445.2.a.bp	\(4\)	\(43.479\)	4.4.725.1	None	\(1\)	\(0\)	\(4\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5445.2.a.bq	\(4\)	\(43.479\)	\(\Q(\zeta_{15})^+\)	None	\(1\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+(-\beta _{2}-\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
5445.2.a.br	\(4\)	\(43.479\)	4.4.5725.1	None	\(1\)	\(0\)	\(4\)	\(8\)	\(-\)	\(-\)	\(-\)	\(q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bs	\(4\)	\(43.479\)	4.4.48704.2	None	\(2\)	\(0\)	\(-4\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
5445.2.a.bt	\(4\)	\(43.479\)	4.4.725.1	None	\(3\)	\(0\)	\(-4\)	\(-6\)	\(-\)	\(+\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
5445.2.a.bu	\(4\)	\(43.479\)	4.4.2525.1	None	\(3\)	\(0\)	\(-4\)	\(-11\)	\(-\)	\(+\)	\(-\)	\(q+(1+\beta _{2}-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{3})q^{4}+\cdots\)
5445.2.a.bv	\(4\)	\(43.479\)	4.4.725.1	None	\(5\)	\(0\)	\(4\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
5445.2.a.bw	\(6\)	\(43.479\)	6.6.74043072.1	None	\(0\)	\(0\)	\(-6\)	\(0\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
5445.2.a.bx	\(6\)	\(43.479\)	6.6.27433728.1	None	\(0\)	\(0\)	\(-6\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots\)
5445.2.a.by	\(6\)	\(43.479\)	6.6.74043072.1	None	\(0\)	\(0\)	\(6\)	\(0\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
5445.2.a.bz	\(6\)	\(43.479\)	6.6.437199552.1	None	\(0\)	\(0\)	\(-6\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
5445.2.a.ca	\(8\)	\(43.479\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-4\)	\(0\)	\(-8\)	\(8\)	\(+\)	\(+\)	\(+\)	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cb	\(8\)	\(43.479\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-4\)	\(0\)	\(8\)	\(-8\)	\(+\)	\(-\)	\(-\)	\(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5445.2.a.cc	\(8\)	\(43.479\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(4\)	\(0\)	\(-8\)	\(-8\)	\(+\)	\(+\)	\(-\)	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
5445.2.a.cd	\(8\)	\(43.479\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(4\)	\(0\)	\(8\)	\(8\)	\(+\)	\(-\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots\)